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Escape Dynamics in Learning Models

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  • Noah Williams

Abstract

This article illustrates and characterizes how adaptive learning can lead to recurrent large fluctuations. Learning models have typically focused on the convergence of beliefs towards an equilibrium. However in stochastic environments, there may be rare but recurrent episodes where shocks cause beliefs to escape from the equilibrium, generating large movements in observed outcomes. I characterize the escape dynamics by drawing on the theory of large deviations, developing new results which make this theory directly applicable in a class of learning models. The likelihood, frequency, and most likely direction of escapes are all characterized by a deterministic control problem. I illustrate my results with two simple examples.

Suggested Citation

  • Noah Williams, 2019. "Escape Dynamics in Learning Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(2), pages 882-912.
    • Handle: RePEc:oup:restud:v:86:y:2019:i:2:p:882-912.
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    File URL: http://hdl.handle.net/10.1093/restud/rdy033
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    Citations

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    Cited by:

    1. Jaqueson K. Galimberti, 2020. "Information weighting under least squares learning," CAMA Working Papers 2020-46, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. George W. Evans & Seppo Honkapohja & Kaushik Mitra, 2022. "Expectations, Stagnation, And Fiscal Policy: A Nonlinear Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(3), pages 1397-1425, August.
    3. Williams, Noah, 2022. "Learning and equilibrium transitions: Stochastic stability in discounted stochastic fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 145(C).
    4. Evans, David & Li, Jungang & McGough, Bruce, 2023. "Local rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 216-236.
    5. Galimberti, Jaqueson K., 2019. "An approximation of the distribution of learning estimates in macroeconomic models," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 29-43.
    6. Nan Li & Chris Papageorgiou & Tong Xu & Tao Zha, 2021. "The S-curve: Understanding the Dynamics of Worldwide Financial Liberalization," NBER Working Papers 28994, National Bureau of Economic Research, Inc.
    7. Evans, David & Evans, George W. & McGough, Bruce, 2022. "The RPEs of RBCs and other DSGEs," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    8. Evans, David & Evans, George W. & McGough, Bruce, 2021. "Learning when to say no," Journal of Economic Theory, Elsevier, vol. 194(C).

    More about this item

    Keywords

    Learning; Dynamics; Fluctuations;
    All these keywords.

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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